Shape transition and oblate-prolate coexistence in N=Z fpg-shell nuclei

Nuclear shape transition and oblate-prolate coexistence in $N=Z$ nuclei are investigated within the configuration space ($2p_{3/2}$, $1f_{5/2}$, $2p_{1/2}$, and $1g_{9/2}$). We perform shell model calculations for $^{60}$Zn, $^{64}$Ge, and $^{68}$Se and constrained Hartree-Fock (CHF) calculations for $^{60}$Zn, $^{64}$Ge, $^{68}$Se, and $^{72}$Kr, employing an effective pairing plus quadrupole residual interaction with monopole interactions. The shell model calculations reproduce well the experimental energy levels of these nuclei. From the analysis of potential energy surface in the CHF calculations, we found shape transition from prolate to oblate deformation in these $N=Z$ nuclei and oblate-prolate coexistence at $^{68}$Se. The ground state of $^{68}$Se has oblate shape, while the shape of $^{60}$Zn and $^{64}$Ge are prolate. It is shown that the isovector matrix elements between $f_{5/2}$ and $p_{1/2}$ orbits cause the oblate deformation for $^{68}$Se, and four-particle four-hole ($4p-4h$) excitations are important for the oblate configuration.Comment: 6 pages, 5 figures, accepted for publication in Phys. Rev.

Extrapolation method in shell model calculations with deformed basis

An extrapolation method in shell model calculations with deformed basis is presented, which uses a scaling property of energy and energy variance for a series of systematically approximated wave functions to the true one. Such approximated wave functions are given by variation-after-projection method concerning the full angular momentum projection. This extrapolation needs energy variance, which amounts to the calculation of expectation value of square of Hamiltonian $\hat{H}^2$. We present the method to evaluate this matrix element and show that large reduction of its numerical computation can be done by taking an advantage of time-reversal symmetry. The numerical tests are presented for $fp$ shell calculations with a realistic residual interaction.Comment: 5 pages, 2 figures, accepted for publication in Phys. Rev.

Nuclear Shell Model by the Quantum Monte Carlo Diagonalization Method

The feasibility of shell-model calculations is radically extended by the Quantum Monte Carlo Diagonalization method with various essential improvements. The major improvements are made in the sampling for the generation of shell-model basis vectors, and in the restoration of symmetries such as angular momentum and isospin. Consequently the level structure of low-lying states can be studied with realistic interactions. After testing this method on $^{24}$Mg, we present first results for energy levels and $E2$ properties of $^{64}$Ge, indicating its large and $\gamma$-soft deformation.Comment: 12 pages, RevTex, 2 figures, to be published in Physical Review Letter

Experimental evidence for 56Ni-core breaking from the low-spin structure of the N=Z nucleus 58Cu

Low-spin states in the odd-odd N=Z nucleus 58Cu were investigated with the 58Ni(p,n gamma)58Cu fusion evaporation reaction at the FN-tandem accelerator in Cologne. Seventeen low spin states below 3.6 MeV and 17 new transitions were observed. Ten multipole mixing ratios and 17 gamma-branching ratios were determined for the first time. New detailed spectroscopic information on the 2+,2 state, the Isobaric Analogue State (IAS) of the 2+,1,T=1 state of 58Ni, makes 58Cu the heaviest odd-odd N=Z nucleus with known B(E2;2+,T=1 --> 0+,T=1) value. The 4^+ state at 2.751 MeV, observed here for the first time, is identified as the IAS of the 4+,1,T=1 state in 58Ni. The new data are compared to full pf-shell model calculations with the novel GXPF1 residual interaction and to calculations within a pf5/2 configurational space with a residual surface delta interaction. The role of the 56Ni core excitations for the low-spin structure in 58Cu is discussed.Comment: 15 pages, 7 figures, submitted to Phys. Rev.

Effective mass staircase and the Fermi liquid parameters for the fractional quantum Hall composite fermions

Effective mass of the composite fermion in the fractional quantum Hall system, which is of purely interaction originated, is shown, from a numerical study, to exhibit a curious nonmonotonic behavior with a staircase correlated with the number (=2,4,...) of attached flux quanta. This is surprising since the usual composite-fermion picture predicts a smooth behavior. On top of that, significant interactions are shown to exist between composite fermions, where the excitation spectrum is accurately reproduced in terms of Landau's Fermi liquid picture with negative (i.e., Hund's type) orbital and spin exchange interactions.Comment: 4 pages, 3 figures, REVTe

Variational Monte Carlo Study of Electron Differentiation around Mott Transition

We study ground-state properties of the two-dimensional Hubbard model at half filling by improving variational Monte Carlo method and by implementing quantum-number projection and multi-variable optimization. The improved variational wave function enables a highly accurate description of the Mott transition and strong fluctuations in metals. We clarify how anomalous metals appear near the first-order Mott transition. The double occupancy stays nearly constant as a function of the on-site Coulomb interaction in the metallic phase near the Mott transition in agreement with the previous unbiased results. This unconventional metal at half filling is stabilized by a formation of ``electron-like pockets'' coexisting with an arc structure, which leads to a prominent differentiation of electrons in momentum space. An abrupt collapse of the ``pocket'' and ``arc'' drives the first-order Mott transition.Comment: 4 pages, 3 figure

Critical Casimir effect and wetting by helium mixtures

We have measured the contact angle of the interface of phase-separated $^{3}$He-$^{4}$He mixtures against a sapphire window. We have found that this angle is finite and does not tend to zero when the temperature approaches $T_t$, the temperature of the tri-critical point. On the contrary, it increases with temperature. This behavior is a remarkable exception to what is generally observed near critical points, i.e. "critical point wetting''. We propose that it is a consequence of the "critical Casimir effect'' which leads to an effective attraction of the $^{3}$He-$^{4}$He interface by the sapphire near $T_{t}$.Comment: submitted july 13 (2002), published march 20 (2003

Magic numbers in exotic nuclei and spin-isospin properties of {\it NN} interaction

The magic numbers in exotic nuclei are discussed, and their novel origin is shown to be the spin-isospin dependent part of the nucleon-nucleon interaction in nuclei. The importance and robustness of this mechanism is shown in terms of meson exchange, G-matrix and QCD theories. In neutron-rich exotic nuclei, magic numbers such as N = 8, 20, etc. can disappear, while N = 6, 16, etc. arise, affecting the structure of lightest exotic nuclei to nucleosynthesis of heavy elements.Comment: 4 pages, 3 figures, revte

Level spacing distribution of pseudointegrable billiard

In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for $S>1$, although the level repulsion still remains in the small $S$ region. The difference from the previous works is analyzed in detail.Comment: 11 pages, REVTeX file, 3 PostScript Figure

Mott Transition in the Hubbard Model on Checkerboard Lattice

We investigate the bandwidth-controlled Mott transition in the Hubbard model on the checkerboard lattice at half filling using the path-integral renormalization group (PIRG) method. It is demonstrated that the system undergoes a first-order phase transition to the plaquette-singlet insulating phase at a finite Hubbard interaction. This conclusion is drawn via a detailed analysis of the spin and charge correlations around the phase transition point by means of the PIRG method aided with a new iteration scheme introduced in this paper.Comment: 7pages, 9figures, accepted for publication in J. Phys. Soc. Jp